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Jankov-style Formulas and Refutation Systems
Jankov-style Formulas and Refutation Systems

Author(s): Alex Citkin
Subject(s): Philosophy
Published by: Wydawnictwo Uniwersytetu Jagiellońskiego

Summary/Abstract: The paper studies the logics which algebraic semantics comprises of the Hilbert algebras endowed with additional operations - the regular algebras. With any finite subdirectly irreducible regular algebra one can associate a Jankov formula. In its turn, the Jankov formulas can be used as anti-axioms for a refutation system. It is proven that a logic has a complete refutation system based on Jankov formulas if and only if this logic enjoys finite model property. Also, such a refutation system is finite, that is, it contains a finite number of axioms and anti-axioms, if and and only if the logic is tabular.

  • Issue Year: 2013
  • Issue No: 48
  • Page Range: 67-80
  • Page Count: 14
  • Language: English